Write \( 1011101_{2} \) in deci

We are given the binary number \[ 1011101_2. \] We convert it to decimal by expanding it as a sum of powers of 2. Write the number with its digits and corresponding exponents: \[ \begin{array}{ccccccc} 1 & 0 & 1 & 1 & 1 & 0 & 1 \\ 2^6 & 2^5 & 2^4 & 2^3 & 2^2 & 2^1 & 2^0 \\ \end{array} \] Multiply each binary digit by its corresponding power of 2: \[ \begin{aligned} 1 \times 2^6 &= 1 \times 64 = 64, \\ 0 \times 2^5 &= 0 \times 32 = 0, \\ 1 \times 2^4 &= 1 \times 16 = 16, \\ 1 \times 2^3 &= 1 \times 8 = 8, \\ 1 \times 2^2 &= 1 \times 4 = 4, \\ 0 \times 2^1 &= 0 \times 2 = 0, \\ 1 \times 2^0 &= 1 \times 1 = 1. \end{aligned} \] Now, sum these values: \[ 64 + 0 + 16 + 8 + 4 + 0 + 1 = 93. \] Thus, the binary number \(1011101_2\) in decimal is \[ 93_{10}. \]